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1
Du, Qin Jun, Xue Yi Zhang, and Shi Long Zhai. "Humanoid Robot Arm Kinematics Modeling and Motion Planning." Applied Mechanics and Materials 644-650 (September 2014): 247–50. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.247.
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This paper establishes the kinematics model of humanoid robot arm, the arm forward kinematics equations were built and solved, based on the advantages of CCD (Cyclic Coordinate Descent) and BFS (Broyden-Fletcher-Shanno) algorithm to solve the inverse kinematics of humanoid robot arm. In the joint space, using cubic polynomial and quintic polynomial interpolation method respectively for each joint angle interpolation. Cubic polynomial trajectory planning can meet the point-to-point movement in general, but can not guarantee the continuity of acceleration of each point; Quintic polynomial trajectory planning can ensure that each point is continuous of the joint angle, angular velocity, and angular acceleration, so this polynomial method can meet the movement of the humanoid robot arm.
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Sun, Jun, Ling Lu, Jun Qing Chen, and Jiu Fu Jin. "Analysis of Gait Planning Method for Biped Robots." Advanced Materials Research 753-755 (August 2013): 1995–2000. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.1995.
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Biped robots research is mainly concentrated on the control system development and doing simulation, cubic spline interpolation method is widely applied to pre-gait planning work. This paper analyzed the robots walking process and calculated the joint trajectory curves of a walk cycle by using spline interpolation and the quintic polynomial fitting means, verifies that the result obtained by quintic polynomial algorithm tends to be more ideal, it is conducive to maintain walking stability and find the optimal joint angles. The paper provides a theoretical basis for optimizing robots trajectory planning.
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Shijie, Li. "Research Progress on Trajectory Planning of Industrial Robots." Current Journal of Applied Science and Technology 42, no. 2 (2023): 25–36. http://dx.doi.org/10.9734/cjast/2023/v42i24052.
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The research status of industrial robot trajectory planning is discussed in detail, and the applicable occasions of cubic polynomial interpolation, quintic polynomial interpolation, B-spline curve, mixed polynomial interpolation and other methods commonly used in basic trajectory planning are comprehensively analyzed. At the same time, various methods of optimal trajectory planning for industrial robots are comprehensively reviewed. The advantages and disadvantages of various methods are compared and the important research direction of optimal trajectory planning is prospected.
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Zhang, Yuelou, Lingshan Chen, and Ning Li. "Improved Quintic Polynomial Autonomous Vehicle Lane-Change Trajectory Planning Based on Hybrid Algorithm Optimization." World Electric Vehicle Journal 16, no. 5 (2025): 244. https://doi.org/10.3390/wevj16050244.
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A trajectory planning method is proposed to address the lane-changing problem in intelligent vehicles. The method is based on quintic polynomial improvement. The transit position is determined according to the position and state of motion of the vehicle and the obstacle vehicle; the lane-changing process is divided into two segments. The quintic polynomials are commonly applied in trajectory planning, respectively, in the two segments. According to the different characteristics of the lane-changing paths in the front and rear segments, a multi-objective optimization function with different weight coefficients is established. A safe and comfortable lane-changing trajectory is achieved through the improved particle swarm optimization algorithm. Real-time simulation tests of lane-changing method are conducted on the hardware-in-the-loop platform. The method can be used in different scenarios to plan safe and comfortable trajectories.
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Yang, Can, and Jie Liu. "Trajectory Tracking Control of Intelligent Driving Vehicles Based on MPC and Fuzzy PID." Mathematical Problems in Engineering 2023 (February 3, 2023): 1–24. http://dx.doi.org/10.1155/2023/2464254.
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To improve the stability and accuracy of quintic polynomial trajectory tracking, an MPC (model predictive control) and fuzzy PID (proportional-integral-difference)- based control method are proposed. A lateral tracking controller is designed by using MPC with rule-based horizon parameters. The lateral tracking controller controls the steering angle to reduce the lateral tracking errors. A longitudinal tracking controller is designed by using a fuzzy PID. The longitudinal controller controls the motor torque and brake pressure referring to a throttle/brake calibration table to reduce the longitudinal tracking errors. By combining the two controllers, we achieve satisfactory trajectory tracking control. Relative vehicle trajectory tracking simulation is carried out under common scenarios of quintic polynomial trajectory in the Simulink/Carsim platform. The result shows that the strategy can avoid excessive trajectory tracking errors which ensures a better performance for trajectory tracking with high safety, stability, and adaptability.
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Zhang, Wenjia, Weiwei Shang, Bin Zhang, Fei Zhang, and Shuang Cong. "Stiffness-based trajectory planning of a 6-DOF cable-driven parallel manipulator." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 21 (2016): 3999–4011. http://dx.doi.org/10.1177/0954406216659893.
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The stiffness of the cable-driven parallel manipulator is usually poor because of the cable flexibility, and the existing methods on trajectory planning mainly take the minimum time and the optimal energy into account, not the stiffness. To solve it, the effects of different trajectories on stiffness are studied for a six degree-of-freedom cable-driven parallel manipulator, according to the kinematic model and the dynamic model. The condition number and the minimum eigenvalue of the dimensionally homogeneous stiffness matrix are selected as performance indices to analyze the stiffness changes during the motion. The simulation experiments are implemented on a six degree-of-freedom cable-driven parallel manipulator, to study the stiffness of three different trajectory planning approaches such as S-type velocity profile, quintic polynomial, and trigonometric function. The accelerations of different methods are analyzed, and the stiffness performances for the methods are compared after planning the point-to-point straight and the curved trajectories. The simulation results indicate that the quintic polynomial and S-type velocity profile have the optimal performance to keep the stiffness stable during the motion control and the travel time of the quintic polynomial can be optimized sufficiently while keeping stable.
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Li, Yang, Linbo Li, and Daiheng Ni. "Dynamic Trajectory Planning for Automated Lane Changing Using the Quintic Polynomial Curve." Journal of Advanced Transportation 2023 (September 15, 2023): 1–14. http://dx.doi.org/10.1155/2023/6926304.
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As one of the key algorithms in supporting AV (autonomous vehicle) to complete the LC (lane changing) maneuver, the LTP (LC trajectory planning) algorithm generates safe and efficient LC trajectory for the AV. This paper proposes a novel dynamic LTP algorithm based on the quintic polynomial curve. This algorithm is capable of adjusting LC trajectory according to the state changes of the surrounding driving environment. The formulation of our proposed algorithm mainly consists the underlying form of trajectory equation, the optimization objective function, the corresponding constrains, and the SQP (sequential quadratic programming) algorithm. For each planning step, the time-based quintic polynomial function is introduced to model the trajectory equation. The problem of solving the parameters of the corresponding equation is then transformed into an optimization problem, which takes driver’s safety, comfort, and efficiency into account. After that, the SQP algorithm is employed to solve this optimization problem. Finally, both numerical simulation and field-data validation are used to verify the effectiveness of our proposed algorithm. We anticipate that the research could provide certain valuable insights for developing more reliable LC algorithms for AVs.
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Reddy, A. Sridhar, V. V. M. J. Satish Chembuly, and V. V. S. Kesava Rao. "Modelling and Simulation of a Redundant Agricultural Manipulator with Virtual Prototyping." Journal of Robotics and Control (JRC) 4, no. 1 (2023): 83–94. http://dx.doi.org/10.18196/jrc.v4i1.17121.
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The development of autonomous robots for agricultural applications includes motion planning, fruit picking, and collision avoidance with surrounding environments, and these become challenging tasks. For harvesting applications, robust control of the manipulator is needed for the effective motion of the robot. Several combinations of Proportional(P)- Integrative(I)- Derivative(D) controllers are modelled and a simulation study was performed for trajectory tracking of a redundant manipulator in virtual agricultural environments. The article presents a comprehensive study on kinematic modelling and dynamic control of redundant manipulator for fruit-picking applications in virtual environments. The collisions with surrounding environment were eliminated using ‘bounding box technique’. The joint variables are obtained by constructing Inverse Kinematics (IK) problem and are determined using a classical optimization technique. Different controllers are modelled in the ‘Simulink’ environment and are tuned to generate error-free trajectory tracking during harvesting. The task space locations (TSLs) are considered as via-points, and joint variables at each TSLs are obtained by Sequential Quadratic Programming (SQP) technique. Joint-level trajectories are generated using Quintic and B-spline polynomials. For effective trajectory tracking, torque variations are controlled using the PID and Feedforward (FF) controller. The dynamic simulations of the robot manipulator are performed in Simscape Multibody software. Results show that the during the trajectory tracking of the manipulator, the Feed-forward controller performs best with Quintic polynomial trajectory.
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Zeng, Xinhong, and Yongxiang Wang. "Analysis and Simulation of Polishing Robot Operation Trajectory Planning." Algorithms 18, no. 1 (2025): 53. https://doi.org/10.3390/a18010053.
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Trajectory planning is essential for robotic polishing tasks, as the effectiveness of this planning directly influences the quality of the work and the energy efficiency of the operation. This study introduces an innovative trajectory planning method for robotic polishing tasks, focusing on the development and application of quintic B-spline interpolation. Recognizing the critical impact of trajectory planning on the quality and energy efficiency of robotic operations, we analyze the structure and parameters of the ABB-IRB120 robot within a laboratory setting. Using the Denavit–Hartenberg parameter method, a kinematic model is established, and the robot’s motion equations are derived through matrix transformation. We then propose a novel approach by implementing both fifth-degree polynomial and quintic B-spline interpolation algorithms for planning the robot’s spatial spiral arc trajectory, which is a key contribution of this work. The effectiveness of these methodologies is validated through simulation in MATLAB’s robotics toolbox. Our findings demonstrate that the quintic B-spline interpolation not only significantly improves task precision but also optimizes energy consumption, making it a superior method for trajectory planning in robotic grinding applications. By integrating advanced interpolation techniques, this study provides substantial technological and environmental benefits, offering a groundbreaking reference for enhancing the precision and efficiency of robotic control systems.
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Ma, Jun, Jian Ping Hu, Xiao Yue Yan, Chun Hui Qi, and Jing Guan. "Transplanting Path Planning and Motion Functions Research of the High-Speed Tray Seedling Transplanting Robot." Advanced Materials Research 694-697 (May 2013): 1747–52. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.1747.
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High-speed tray seedling transplanting robot was developed which used two-DOF parallel mechanism as transplanting mechanism, and pneumatic manipulator as the end-effector, so it can achieve high speed of transplanting. According to transplanting seedlings from high-density plug to the low-density plug, a type of transplanting path was put forward which consists of rise, translation and decline, in this paper, it was called three-stage trajectory. Analysis the movement characteristic of each stage, make sure the stability of transplanting, then the sine motion law, quintic polynomial motion law and septic polynomial motion law were put forward as the Transplanting movement function according the analysis of movement characteristic. Compared the transplanting efficiency and stability of the three motion law through their velocity, acceleration and saltus, finally, quintic polynomial motion law was preferred as transplanting robot motion law. Transplanting experiment was taken on the developed prototype, the transplanting frequency was more than 60 per minute and the qualified rate can reach 92.71%.
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Wang, Dawei, Hongliang Guo, Gang Li, Fukuo Ma, Yahui Xu, and Jian Wu. "Comfort-Based Intelligent Vehicle Trajectory Planning in High-Speed Scenarios." Journal of Physics: Conference Series 2999, no. 1 (2025): 012012. https://doi.org/10.1088/1742-6596/2999/1/012012.
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Abstract To solve the situation of uncomfortable feelings for drivers and passengers during the lane-changing(LC) process of autonomous vehicles in high-speed scenarios, the trajectory of quintic polynomial planning is effectively optimized. Through the analysis of the fifth-degree polynomial equation and the transverse force coefficient in the process of vehicle driving, and optimal trajectory is constructed with the constraints of the LC time and the relevant comfort indexes of the vehicle LC process, transverse angular velocity, transverse acceleration, and transverse acceleration as the constraints. Finally, the simulation scene is constructed by Prescan, and the nonlinear planning toolbox in MATLAB was employed to ascertain the unknown parameters, thereby determining the optimal lane change time and trajectory. The results show that the trajectory planning meets the vehicle LC requirements under real-world conditions, demonstrating good maneuvering stability and fulfilling the comfort criteria for the LC process.
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Vu, Trieu Minh, Reza Moezzi, Jindrich Cyrus, Jaroslav Hlava, and Michal Petru. "Feasible Trajectories Generation for Autonomous Driving Vehicles." Applied Sciences 11, no. 23 (2021): 11143. http://dx.doi.org/10.3390/app112311143.
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This study presents smooth and fast feasible trajectory generation for autonomous driving vehicles subject to the vehicle physical constraints on the vehicle power, speed, acceleration as well as the hard limitations of the vehicle steering angle and the steering angular speed. This is due to the fact the vehicle speed and the vehicle steering angle are always in a strict relationship for safety purposes, depending on the real vehicle driving constraints, the environmental conditions, and the surrounding obstacles. Three different methods of the position quintic polynomial, speed quartic polynomial, and symmetric polynomial function for generating the vehicle trajectories are presented and illustrated with simulations. The optimal trajectory is selected according to three criteria: Smoother curve, smaller tracking error, and shorter distance. The outcomes of this paper can be used for generating online trajectories for autonomous driving vehicles and auto-parking systems.
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Analooee, Ali, Reza Kazemi, and Shahram Azadi. "SCR-Normalize: A novel trajectory planning method based on explicit quintic polynomial curves." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 234, no. 4 (2020): 650–74. http://dx.doi.org/10.1177/1464419320924196.
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This paper presents a framework for generating explicit quintic polynomial curves as the trajectory of autonomous vehicles. The method is called SCR-Normalize and is founded on two novel ideas. The first concept is to rotate the coordinate reference, regarding the boundary conditions, in order to reach a special coordinate reference called Secondary Coordinate Reference (SCR). In the SCR, the explicit quintic polynomial curve has short length and low curvature values (i.e. the curve is not wiggly). The second concept is to normalize the trajectory in order to speed up the framework. Two kinds of problems are considered to be solved in this paper: (a) generating a length optimal trajectory for arbitrary boundary conditions subject to a curvature constraint; and (b) path smoothing. For case (a), for the lane change manoeuvre, the problem is solved explicitly. In addition, the familiar expression for the optimal interval of the lane change manoeuvre is analytically proved for the first time. For arbitrary swerving manoeuvres, two algorithms are presented and their performance is compared with each other and with two other algorithms. Similarly, for case (b), an algorithm is presented and its performance is compared with three other methods. Evaluating the algorithms in the examples, and comparing the results with other methods illustrates the efficiency of the SCR-Normalize framework to generate optimal trajectories in real time.
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Deng, Huan, Jian Wang, Jun Yang, Ruofei Du, Zhenyang Hai, and Yunjing wang. "Study on automatic lane change trajectory control of intelligent vehicle on expressway." Journal of Physics: Conference Series 2480, no. 1 (2023): 012003. http://dx.doi.org/10.1088/1742-6596/2480/1/012003.
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Abstract Aiming at the dangerous working condition of the front car driving at low speed, a safety distance model using the vehicle braking process is proposed to determine the best time for intelligent vehicles to change lanes. Based on the fitting method of quintic polynomial, an automatic lane change fitting trajectory is constructed, and the LQR algorithm is used to achieve accurate tracking. Through the joint simulation and experiment of CarSim, PreScan, and MATLAB/Simulink, it is shown that the established lane change trajectory control model can determine the best time for intelligent vehicles to change lanes, plan safe and comfortable lane change trajectory, and achieve good tracking effect.
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Liang, Xu, and Tingting Su. "Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint." Applied Sciences 9, no. 21 (2019): 4491. http://dx.doi.org/10.3390/app9214491.
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A new trajectory planning approach on the basis of the quintic Pythagorean–Hodograph (PH) curve is presented and applied to Delta robot for implementing pick-and-place operation (PPO). To satisfy a prescribed geometrical constraint, which indicates the distance between the transition segment curve and right angle of PPO trajectory is no greater than a prescribed value, the quintic PH curve is used to produce a connection segment path for collision avoidance. The relationship between the PH curve and constraint is analyzed, based on which PH curve is calculated simply. Afterwards, the trajectory is planned in different phases with different motion laws, i.e. polynomial motion laws and PH curve parameter-dependent motion laws, to obtain a smooth performance both in Cartesian and joint space. The relationship between the PH curve and constraint is also used to improve the efficiency of calculation, and the trajectory symmetry is used to reduce calculation time by direct symmetric transformation. Thus, real-time performance is improved. The results of simulations and experiments indicate that the approach in this paper can provide smooth motion and meet the real-time requirement under the prescribed geometrical constraint.
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Zhao, Jianwei, Tao Han, Xiaofei Ma, et al. "Research on Kinematics Analysis and Trajectory Planning of Novel EOD Manipulator." Applied Sciences 11, no. 20 (2021): 9438. http://dx.doi.org/10.3390/app11209438.
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To address the problems of mismatch, poor flexibility and low accuracy of ordinary manipulators in the complex special deflagration work process, this paper proposes a new five-degree-of-freedom (5-DOF) folding deflagration manipulator. Firstly, the overall structure of the explosion-expulsion manipulator is introduced. The redundant degrees of freedom are formed by the parallel joint axes of the shoulder joint, elbow joint and wrist pitching joint, which increase the flexibility of the mechanism. Aiming at a complex system with multiple degrees of freedom and strong coupling of the manipulator, the virtual joint is introduced, the corresponding forward kinematics model is established by D–H method, and the inverse kinematics solution of the manipulator is derived by analytical method. In the MATLAB platform, the workspace of the manipulator is analyzed by Monte Carlo pseudo-random number method. The quintic polynomial interpolation method is used to simulate the deflagration task in joint space. Finally, the actual prototype experiment is carried out using the data obtained by simulation. The trajectory planning using the quintic polynomial interpolation method can ensure the smooth movement of the manipulator and high accuracy of operation. Furthermore, the trajectory is basically consistent with the simulation trajectory, which can realize the work requirements of putting the object into the explosion-proof tank. The new 5-DOF folding deflagration manipulator designed in this paper has stable motion and strong robustness, which can be used for deflagration during the COVID-19 epidemic.
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Xu, Jing, Chaofan Ren, and Xiaonan Chang. "Robot Time-Optimal Trajectory Planning Based on Quintic Polynomial Interpolation and Improved Harris Hawks Algorithm." Axioms 12, no. 3 (2023): 245. http://dx.doi.org/10.3390/axioms12030245.
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Time-optimal trajectory planning is one of the most important ways to improve work efficiency and reduce cost and plays an important role in practical application scenarios of robots. Therefore, it is necessary to optimize the running time of the trajectory. In this paper, a robot time-optimal trajectory planning method based on quintic polynomial interpolation and an improved Harris hawks algorithm is proposed. Interpolation with a quintic polynomial has a smooth angular velocity and no acceleration jumps. It has widespread application in the realm of robot trajectory planning. However, the interpolation time is usually obtained by testing experience, and there is no unified criterion to determine it, so it is difficult to obtain the optimal trajectory running time. Because the Harris hawks algorithm adopts a multi-population search strategy, compared with other swarm intelligent optimization algorithms such as the particle swarm optimization algorithm and the fruit fly optimization algorithm, it can avoid problems such as single population diversity, low mutation probability, and easily falling into the local optimum. Therefore, the Harris hawks algorithm is introduced to overcome this problem. However, because some key parameters in HHO are simply set to constant or linear attenuation, efficient optimization cannot be achieved. Therefore, the nonlinear energy decrement strategy is introduced in the basic Harris hawks algorithm to improve the convergence speed and accuracy. The results show that the optimal time of the proposed algorithm is reduced by 1.1062 s, 0.5705 s, and 0.3133 s, respectively, and improved by 33.39%, 19.66%, and 12.24% compared with those based on particle swarm optimization, fruit fly algorithm, and Harris hawks algorithms, respectively. In multiple groups of repeated experiments, compared with particle swarm optimization, the fruit fly algorithm, and the Harris hawks algorithm, the computational efficiency was reduced by 4.7019 s, 1.2016 s, and 0.2875 s, respectively, and increased by 52.40%, 21.96%, and 6.30%. Under the optimal time, the maximum angular displacement, angular velocity, and angular acceleration of each joint trajectory meet the constraint conditions, and their average values are only 75.51%, 38.41%, and 28.73% of the maximum constraint. Finally, the robot end-effector trajectory passes through the pose points steadily and continuously under the cartesian space optimal time.
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Chang, Qing, Huaiwen Wang, Dongai Wang, Haijun Zhang, Keying Li, and Biao Yu. "Motion Planning for Vibration Reduction of a Railway Bridge Maintenance Robot with a Redundant Manipulator." Electronics 10, no. 22 (2021): 2793. http://dx.doi.org/10.3390/electronics10222793.
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Motivated by the potential applications of maintenance and inspection tasks for railway bridges, we have developed a biped climbing robot. The biped climbing robot can climb on the steel guardrail of the railway bridge with two electromagnetic feet and implement the maintenance and inspection tasks by a redundant manipulator with 7 degrees of freedom. To reduce the vibration of the manipulator caused by the low rigidity of the guardrail and the discontinuous trajectories of joints, a motion planning algorithm for vibration reduction is proposed in this paper. A geometric path accounting for obstacle avoidance and the manipulator’s center of gravity is determined by the gradient projection method with a singularity-robust inverse. Then, a piecewise quintic polynomial S shape curve with a smooth jerk (derivative of joint angular acceleration) profile is used to interpolate the sequence of joint angular position knots that are transformed from the via-points in the obstacle-avoidance path. The parameters of the quintic polynomial S-curve are determined by a nonlinear programming problem in which the objective function is to minimize the maximus of the torque exerted by the manipulator on the guardrail throughout the jerk-continuous trajectory. Finally, a series of simulation experiments are conducted to validate the effectiveness of the proposed algorithm. The simulation results show that the tracking errors of the trajectory with the proposed optimization algorithm are significantly smaller than the tracking errors of the trajectory without optimization. The absolute values of mean deviation of the tracking errors of the three coordinate axes decreased by at least 48.3% compared to the trajectory without vibration-reduction in the triangle working path and linear working path trajectory following simulations. The analysis results prove that the proposed algorithm can effectively reduce the vibration of the end effector of the manipulator.
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Zhang, En Guang. "Design of the Oscillating Follower Cam Profile Based on NX8.0." Applied Mechanics and Materials 365-366 (August 2013): 57–61. http://dx.doi.org/10.4028/www.scientific.net/amm.365-366.57.
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Based on the principle of reversal method, the Motion Simulation module of NX8.0 is adopted to find the trajectory of the oscillating follower roller center relative to the cam with the IF function driving the oscillating follower .At the same time, the contour line of oscillating follower disk cam is also designed using the quintic polynomial spline curve and the motion simulation is verified. The cam design by the reversal method and the theoretical one are compared and analyzed.
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Yue, Shigang, Dominik Henrich, W. L. Xu, and S. K. Tso. "Point-to-Point trajectory planning of flexible redundant robot manipulators using genetic algorithms." Robotica 20, no. 3 (2002): 269–80. http://dx.doi.org/10.1017/s0263574701003861.
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The paper focuses on the problem of point-to-point trajectory planning for flexible redundant robot manipulators (FRM) in joint space. Compared with irredundant flexible manipulators, a FRM possesses additional possibilities during point-to-point trajectory planning due to its kinematics redundancy. A trajectory planning method to minimize vibration and/or executing time of a point-to-point motion is presented for FRMs based on Genetic Algorithms (GAs). Kinematics redundancy is integrated into the presented method as planning variables. Quadrinomial and quintic polynomial are used to describe the segments that connect the initial, intermediate, and final points in joint space. The trajectory planning of FRM is formulated as a problem of optimization with constraints. A planar FRM with three flexible links is used in simulation. Case studies show that the method is applicable.
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Zhou, Yang. "Research on local trajectory planning of autonomous mobile robots." ITM Web of Conferences 47 (2022): 02029. http://dx.doi.org/10.1051/itmconf/20224702029.
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In the process of autonomous motion, the mobile robot needs real-time local trajectory planning based on the global smooth path and nominal local trajectory tracking. In this paper, the local trajectory planning problem of mobile robot is studied, and the local path represented by quintic polynomial is optimized in Frenet coordinate system with the global smooth path as reference path, then, according to the information of the robot’s pose, velocity and angular velocity, the robot’s velocity is planned according to all kinds of constraints. A LQR closed loop control law is designed to realize the precise tracking of local optimal trajectory, which makes the robot move safely and stably in the dynamic environment. In the “maze” simulation environment, using the Stageros simulator the local trajectory planning algorithm is tested, and the validity and correctness of the algorithm are verified.
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Yan, Jianqiang, Mi Li, Zhongxiang Chen, and Yihang Li. "Design and error compensation of active mechanically automated guided vehicle." Mechanics & Industry 22 (2021): 14. http://dx.doi.org/10.1051/meca/2021011.
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To reduce the navigation control cost, this paper proposes a mechanical guidance control scheme that uses a cam-link mechanism as a steering control mechanism for an automated guided vehicle with a fixed driving path. According to the steering principle, a mathematical model of the steering system and the driving trajectory are established. By setting the boundary conditions, the vehicle trajectory is modeled using a quintic polynomial. The contour of the directional control cam is obtained based on the equation of the vehicle trajectory. Because errors occur in actual machining and assembly processes, errors will be classified based on their impact on the trajectory. The effects of various errors on the trajectory are quantitatively determined by using simulation methods with different parameters. Furthermore, an error compensation approach is designed to reduce the influence of the error on the trajectory directly or indirectly. Finally, experiment results illustrate that the adjustment accuracy of the proposed automated guided vehicle trajectory is 2 mm.
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Chen, Sihan, Changqing Zhang, and Jiaping Yi. "Time-Optimal Trajectory Planning for Woodworking Manipulators Using an Improved PSO Algorithm." Applied Sciences 13, no. 18 (2023): 10482. http://dx.doi.org/10.3390/app131810482.
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Woodworking manipulators are applied in wood processing to promote automatic levels in the wood industry. However, traditional trajectory planning results in low operational stability and inefficiency. Therefore, we propose a method combining 3-5-3 piecewise polynomial (composed of cubic and quintic polynomials) interpolation and an improved particle swarm optimization (PSO) algorithm to study trajectory planning and time optimization of woodworking manipulators. In trajectory planning, we conducted the kinematics analysis to determine the position information of joints at path points in joint space and used 3-5-3 piecewise polynomial interpolation to fit a point-to-point trajectory and ensure the stability. For trajectory time optimization, we propose an improved PSO that adapts multiple strategies and incorporates a golden sine optimization algorithm (Gold-SA). Therefore, the proposed improved PSO can be called GoldS-PSO. Using benchmark functions, we compared GoldS-PSO to four other types of PSO algorithms and Gold-SA to verify its effectiveness. Then, using GoldS-PSO to optimize the running time of each joint, our results showed that GoldS-PSO was superior to basic PSO and Gold-SA. The shortest running time obtained by using GoldS-PSO was 47.35% shorter than before optimization, 8.99% shorter than the basic PSO, and 6.23% shorter than the Gold-SA, which improved the running efficiency. Under optimal time for GoldS-PSO, our simulation results showed that the displacement and velocity of each joint were continuous and smooth, and the acceleration was stable without sudden changes, proving the method’s feasibility and superiority. This study can serve as the basis for the motion control system of woodworking manipulators and provide reference for agricultural and forestry engineering optimization problems.
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He, Chao, Wenhui Jiang, Junting Li, Jian Wei, Jiang Guo, and Qiankun Zhang. "Fuzzy Logic-Based Autonomous Lane Changing Strategy for Intelligent Internet of Vehicles: A Trajectory Planning Approach." World Electric Vehicle Journal 15, no. 9 (2024): 403. http://dx.doi.org/10.3390/wevj15090403.
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The autonomous lane change maneuver is a critical component in the advancement of intelligent transportation systems (ITS). To enhance safety and efficiency in dynamic traffic environments, this study introduces a novel autonomous lane change strategy leveraging a quintic polynomial function. To optimize the trajectory, we formulate an objective function that balances the time required for lane changes with the peak acceleration experienced during the maneuver. The proposed method addresses key challenges such as driver discomfort and prolonged lane change durations by considering the entire lane change process rather than just the initiation point. Utilizing a fifth-order polynomial for trajectory planning, the strategy ensures smooth and continuous vehicle movement, reducing the risk of collisions. The effectiveness of the method is validated through comprehensive simulations and real-world vehicle tests, demonstrating significant improvements in lane change performance. Despite its advantages, the model requires further refinement to address limitations in mixed traffic conditions. This research provides a foundation for developing intelligent vehicle systems that prioritize safety and adaptability.
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Lou, Junqiang, Yanding Wei, Guoping Li, Yiling Yang, and Fengran Xie. "Optimal Trajectory Planning and Linear Velocity Feedback Control of a Flexible Piezoelectric Manipulator for Vibration Suppression." Shock and Vibration 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/952708.
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Trajectory planning is an effective feed-forward control technology for vibration suppression of flexible manipulators. However, the inherent drawback makes this strategy inefficient when dealing with modeling errors and disturbances. An optimal trajectory planning approach is proposed and applied to a flexible piezoelectric manipulator system in this paper, which is a combination of feed-forward trajectory planning method and feedback control of piezoelectric actuators. Specifically, the joint controller is responsible for the trajectory tracking and gross vibration suppression of the link during motion, while the active controller of actuators is expected to deal with the link vibrations after joint motion. In the procedure of trajectory planning, the joint angle of the link is expressed as a quintic polynomial function. And the sum of the link vibration energy is chosen as the objective function. Then, genetic algorithm is used to determine the optimal trajectory. The effectiveness of the proposed method is validated by simulation and experiments. Both the settling time and peak value of the link vibrations along the optimal trajectory reduce significantly, with the active control of the piezoelectric actuators.
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Liu, Shao Gang, Hong Wang Du, Shi Cheng Wang, and Ya Nan Zhao. "Path Planning and System Simulation for an Industrial Spot Welding Robot Based on SimMechanics." Key Engineering Materials 419-420 (October 2009): 665–68. http://dx.doi.org/10.4028/www.scientific.net/kem.419-420.665.
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A robot used for industrial spot welding is a 4-DOF serial mechanism, it can be applied to some special industries. There are multi via points known in path, each joint value can be accurately solved by the inverse kinematics. The quintic polynomial interpolation was adopted between each two adjacent desired via points, the continuous trajectory is formed in accordance with the time course. The simulation model is developed using SimMechnics, the movement parameters and path are obtained by simulating, the simulation results indicate that the motional parameters and path can be accurately and effectively obtained for robot analysis and design.
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Xu, Yong Pan, and Ying Hong. "Time Optimal Path Planning of Palletizing Robot." Applied Mechanics and Materials 470 (December 2013): 658–62. http://dx.doi.org/10.4028/www.scientific.net/amm.470.658.
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In order to improve the efficiency and reduce the vibration of Palletizing Robot, a new optimal trajectory planning algorithm is proposed. This algorithm is applied to the trajectory planning of Palletizing manipulators. The S-shape acceleration and deceleration curve is adopted to interpolate joint position sequences. Considering constraints of joint velocities, accelerations and jerks, the traveling time of the manipulator is minimized. The joint interpolation confined by deviation is used to approximate the straight path, and the deviation is decreased significantly by adding only small number of knots. Traveling time is solved by using quintic polynomial programming strategy between the knots, and then time-jerk optimal trajectories which satisfy constraints are planned. The results show that the method can avoid the problem of manipulator singular points and improve the palletize efficiency.
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Xiwen Guo, Zhou Fang, Qunjing Wang, Siao Wu, and Ronghao Liu. "Smooth Planning for Manipulator with Multi-dimensional Actuator based on Quintic B-spline." Electrotehnica, Electronica, Automatica 70, no. 4 (2022): 20–29. http://dx.doi.org/10.46904/eea.22.70.4.1108003.
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In order to solve the impact problem of uneven velocity during continuous operation for manipulator with multi-dimensional actuator, a smooth planning scheme based on Quintic B-spline algorithm was proposed. Firstly, the physical model of multi-dimensional actuator and its working principle were introduced. At the same time, the motion of the output axis vertex in space was decomposed into three steps, which can make the position relationship between the points more intuitive and convenient for our study. Secondly, the characteristics of Quintic B-spline algorithm were analysed. In this step, the B-spline interpolation function was defined at first, and the basis function of polynomial of degree p was defined according to the relevant information and its characteristics were indicated. Then, we analysed the node sequence parameters. For Quintic B-spline algorithm, when the position sequence of the rotor running track was given, three conditions must be satisfied to uniquely determine the corresponding B-spline function, namely: node vector, control vertex and the degree p of the B-spline curve. On this basis, the boundary constraints and control vertices were solved, which was a very important step. By solving the control vertices of Quintic B-spline curve, a smooth and continuous angular displacement curve can be obtained. The addition of four boundary conditions greatly increases the controllability of the system, making the rotor can start and stop in any way within the constraint conditions, and the connection of each interpolation point is smooth and continuous. The Quintic B-spline algorithm interpolation curve was obtained by simulation based on the time-position sequence of the actuator interpolation points. The results of the interpolation curve verified the effectiveness of the Quintic B-spline algorithm. In addition, three continuous running planning conditions were designed for the same interpolation sequence of the rotor to verify the controllability of the algorithm to the angular velocity and angular acceleration of the rotor during operation. The simulation results show that the Quintic B-spline algorithm has strong controllability for the angular velocity of actuator, and can effectively alleviate the soft impact of the system. Finally, a smooth planning experimental platform with multi-dimensional actuator was built. By setting the same trajectory and different interpolation points, the proposed Quintic B-spline algorithm was compared with the existing S-shaped curve planning algorithm based on the improvement. The results show that the proposed scheme has high control accuracy and strong impact mitigation performance, which can provide a reference for other multi-dimensional actuator trajectory planning.
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Wang, Jian, Qian Li, and Qiyuan Ma. "Research on Active Avoidance Control of Intelligent Vehicles Based on Layered Control Method." World Electric Vehicle Journal 16, no. 4 (2025): 211. https://doi.org/10.3390/wevj16040211.
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To meet the active avoidance requirements of intelligent vehicles, this paper proposes an efficient hierarchical control system. The upper layer generates a safe avoidance trajectory through an optimized path planning algorithm, while the lower layer precisely controls the vehicle to follow the planned path. In the upper layer design, an improved quintic polynomial method is employed to generate the baseline trajectory. By dynamically adjusting lane change duration and utilizing an improved dual-quintic algorithm, collisions with preceding vehicles are effectively avoided. Additionally, a genetic algorithm is applied to automatically optimize parameters, ensuring both driving comfort and planning efficiency. The lower layer control is based on a three-degree-of-freedom monorail vehicle model and the Magic Formula tire model, employing a model predictive control (MPC) approach to continuously correct trajectory deviations in real time, thereby ensuring stable path tracking. To validate the proposed system, a co-simulation environment integrating CarSim, PreScan, and MATLAB was established. The system was tested under various vehicle speeds and road conditions, including wet and dry surfaces. Experimental results demonstrate that the proposed system achieves a path tracking error of less than 0.002 m, effectively reducing accident risks while enhancing the smoothness of the avoidance process. This hierarchical design decomposes the complex avoidance task into planning and control, simplifying system development while balancing safety and real-time performance. The proposed method provides a practical solution for active collision avoidance in intelligent vehicles.
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Yue, Ming, Xiangmin Wu, Lie Guo, and Junjie Gao. "Quintic Polynomial-based Obstacle Avoidance Trajectory Planning and Tracking Control Framework for Tractor-trailer System." International Journal of Control, Automation and Systems 17, no. 10 (2019): 2634–46. http://dx.doi.org/10.1007/s12555-018-0889-9.
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ABDUL JALIL, MUHAMMAD, MUHAMMAD FAHMI MISKON, and MOHD BAZLI BAHAR. "HIGH ACCURACY HUMAN MOTION TRAJECTORY GENERATION FOR EXOSKELETON ROBOT USING CURVE FITTING TECHNIQUE." IIUM Engineering Journal 24, no. 2 (2023): 301–14. http://dx.doi.org/10.31436/iiumej.v24i2.2296.
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Robotic systems often require trajectory planning algorithms that can generate natural human-like movements for tasks such as grasping and manipulation. However, conventional trajectory planning methods may not accurately capture the complex movement patterns observed in humans. In this paper, we present a trajectory planning algorithm based on polynomial curve fitting that aims to address this issue. The algorithm determines the polynomial coefficient values that accurately match the natural human trajectory profile and is evaluated using MATLAB simulations. We compare the proposed algorithm to the conventional quintic polynomial trajectory method, analysing the accuracy, precision, and via-point continuity. The result shows that the algorithm has the ability to generate a trajectory profile with accuracy of 99.8% and a precision of 0.002°. However, the result for via-point continuity shows an error on every sub-phase transition, with the lowest error of 0.0031 between the transition of sub-phases 1 and 2. The result also shows that the lowest fitting error recorded is 0.00014°. The results demonstrate that our algorithm can generate trajectory profiles with higher accuracy and naturalness, potentially improving the performance and usability of robotic systems. ABSTRAK: Sistem robotik sering memerlukan algoritma perancangan trajektori yang dapat menghasilkan gerakan semulajadi seperti manusia bagi tugas seperti memegang dan memanipulasi objek. Walau bagaimanapun, kaedah perancangan trajektori konvensional mungkin tidak dapat merekodkan pola gerakan kompleks seperti yang dihasilkan manusia secara tepat. Kajian ini adalah berkenaan algoritma perancangan lintasan berdasarkan penyepaduan lengkung polinomial bagi menyelesaikan masalah ini. Algoritma ini menentukan nilai pekali polinomial yang sepadan dengan profil gerakan semulajadi manusia dan dinilai menggunakan simulasi MATLAB. Algoritma yang dicadangkan ini telah dibandingkan dengan kaedah perancangan lintasan polinomial kuintik konvensional, dianalisis kejituan, ketepatan, dan keberterusan titik lalu. Keputusan menunjukkan bahawa algoritma tersebut mampu menghasilkan profil lintasan dengan kejituan sebanyak 99.8% dan ketepatan sebanyak 0.002°. Walau bagaimanapun, dapatan kajian mengenai keberterusan titik lalu menunjukkan ralat pada setiap peralihan fasa-sub dengan ralat terendah sebanyak 0.0031 pada peralihan antara fasa-sub 1 dan fasa-sub 2. Dapatan kajian juga menunjukkan bahawa ralat penyepaduan terendah yang direkodkan adalah sebanyak 0.00014°. Keputusan ini menunjukkan bahawa algoritma ini mampu menghasilkan profil lintasan dengan ketepatan dan sifat semula jadi yang lebih tinggi, berpotensi meningkatkan prestasi dan kegunaan sistem robotik.
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Song, Qisong, Shaobo Li, Qiang Bai, et al. "Trajectory Planning of Robot Manipulator Based on RBF Neural Network." Entropy 23, no. 9 (2021): 1207. http://dx.doi.org/10.3390/e23091207.
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Robot manipulator trajectory planning is one of the core robot technologies, and the design of controllers can improve the trajectory accuracy of manipulators. However, most of the controllers designed at this stage have not been able to effectively solve the nonlinearity and uncertainty problems of the high degree of freedom manipulators. In order to overcome these problems and improve the trajectory performance of the high degree of freedom manipulators, a manipulator trajectory planning method based on a radial basis function (RBF) neural network is proposed in this work. Firstly, a 6-DOF robot experimental platform was designed and built. Secondly, the overall manipulator trajectory planning framework was designed, which included manipulator kinematics and dynamics and a quintic polynomial interpolation algorithm. Then, an adaptive robust controller based on an RBF neural network was designed to deal with the nonlinearity and uncertainty problems, and Lyapunov theory was used to ensure the stability of the manipulator control system and the convergence of the tracking error. Finally, to test the method, a simulation and experiment were carried out. The simulation results showed that the proposed method improved the response and tracking performance to a certain extent, reduced the adjustment time and chattering, and ensured the smooth operation of the manipulator in the course of trajectory planning. The experimental results verified the effectiveness and feasibility of the method proposed in this paper.
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Zhu, Zhifang, Yuanjie Liu, Yuling He, et al. "Fuzzy PID Control of the Three-Degree-Of-Freedom Parallel Mechanism Based on Genetic Algorithm." Applied Sciences 12, no. 21 (2022): 11128. http://dx.doi.org/10.3390/app122111128.
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It is necessary to upgrade and transform the sorting equipment in the industrial production line. In order to improve production efficiency and reduce labor intensity, a high-speed lightweight parallel mechanism control system for the high-speed sorting and packaging of light items was studied. A fuzzy PID controller based on genetic algorithm (GA) optimization is proposed according to the nonlinear and strong coupling characteristics of the parallel mechanism (PM) control system. The inverse kinematic analysis was conducted to map the workspace trajectory tracking problem to the joint space. It was transformed into the trajectory planning and solving problems in the joint space. The motion trajectory was obtained utilizing quintic polynomial interpolation. Finally, the servo control system model was established, and the PID control parameters were optimized and self-tuned by the GA. They were applied to the fuzzy PID controller for simulation experiments. The simulation results showed that the GA-optimized fuzzy PID control system compared with the fuzzy PID control system had a 23.39% shorter rise time, 22.32% less regulation time, and 7.18% less steady-state error. The control system had a good dynamic and steady-state performance.
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Zheng, Liyuan, Weiming Liu, and Cong Zhai. "A Dynamic Lane-Changing Trajectory Planning Algorithm for Intelligent Connected Vehicles Based on Modified Driving Risk Field Model." Actuators 13, no. 10 (2024): 380. http://dx.doi.org/10.3390/act13100380.
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A dynamic LC trajectory planning algorithm based on the modified driving risk field is proposed to address the issue of dynamic changes during the lane-changing (LC) process. First, a modified driving risk field (MDRF) model is constructed for LC scenarios. Then, according to the state of the target vehicle and discrete sampling points, a series of LC candidate trajectories were generated based on the quintic polynomial. After eliminating candidate trajectories that do not meet the constraints, the MDRF was utilized as a safety evaluation function. Additionally, comfort and smoothness evaluation functions were combined to evaluate candidate LC trajectories in order to obtain the optimal LC reference trajectory. Then, this paper proposes a dynamic LC trajectory planning algorithm, addressing the challenges of complex traffic scenarios and dynamic changes in adjacent vehicle states. Utilizing the optimal reference trajectory as a basis, a dynamic segmented algorithm is applied to the x–t and y–x curves, constructing an optimized objective function that considers the MDRF. Under multiple constraints, including the continuity and smoothness of the lateral and longitudinal trajectories, the penalty function approach is employed to solve the optimization objective function, yielding the optimal LC trajectory adapted to real-time changes in the traffic state. Finally, the proposed dynamic LC trajectory planning algorithm was validated under four different scenarios by using MATLAB 2023b. The simulation results indicate the safety, continuity, and dynamic feasibility of the proposed algorithm. Moreover, it demonstrates strong adaptability and flexibility in challenging dynamic LC scenarios.
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Liu, Peng, Haibo Tian, Xiangang Cao, et al. "Pick–and–Place Trajectory Planning and Robust Adaptive Fuzzy Tracking Control for Cable–Based Gangue–Sorting Robots with Model Uncertainties and External Disturbances." Machines 10, no. 8 (2022): 714. http://dx.doi.org/10.3390/machines10080714.
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A suspended cable–based parallel robot (CBPR) composed of four cables and an end–grab is employed in a pick–and–place operation of moving target gangues (MTGs) with different shapes, sizes, and masses. This paper focuses on two special problems of pick–and–place trajectory planning and trajectory tracking control of the cable–based gangue–sorting robot in the operation space. First, the kinematic and dynamic models for the cable–based gangue–sorting robots are presented in the presence of model uncertainties and unknown external disturbances. Second, to improve the sorting accuracy and efficiency of sorting system with cable–based gangue–sorting robot, a four-phase pick–and–place trajectory planning scheme based on S-shaped acceleration/deceleration algorithm and quintic polynomial trajectory planning method is proposed, and moreover, a robust adaptive fuzzy tracking control strategy is presented against inevitable uncertainties and unknown external disturbances for trajectory tracking control of the cable–based gangue–sorting robot, where the stability of a closed-loop control scheme is proved with Lyapunov stability theory. Finally, the performances of pick–and–place trajectory planning scheme and robust adaptive tracking control strategy are evaluated through different numerical simulations within Matlab software. The simulation results show smoothness and continuity of pick–and–place trajectory for the end–grab as well as the effectiveness and efficiency to guarantee a stable and accurate pick–and–place trajectory tracking process even in the presence of various uncertainties and external disturbances. The pick–and–place trajectory generation scheme and robust adaptive tracking control strategy proposed in this paper lay the foundation for accurate sorting of MTGs with the robot.
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Wang, Dongyi, Guoli Wang, and Hang Wang. "Optimal Lane Change Path Planning Based on the NSGA-II and TOPSIS Algorithms." Applied Sciences 13, no. 2 (2023): 1149. http://dx.doi.org/10.3390/app13021149.
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Among so many autonomous driving technologies, autonomous lane changing is an important application scenario, which has been gaining increasing amounts of attention from both industry and academic communities because it can effectively reduce traffic congestion and improve road safety. However, most of the existing researchers transform the multi-objective optimization problem of lane changing trajectory into a single objective problem, but how to determine the weight of the objective function is relatively fuzzy. Therefore, an optimization method based on the combination of the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), which provides a new idea for solving the multi-objective optimization problem of lane change trajectory algorithm, is proposed in this paper. Firstly, considering the constraints of lane changing and combining with the collision detection algorithm, the feasible lane changing trajectory cluster is obtained based on the quintic polynomial. In order to ensure the comfort, stability and high efficiency of the lane changing process, the NSGA-II Algorithm is used to optimize the longitudinal displacement and time of lane changing. The continuous ordered weighted averaging (COWA) operator is introduced to calculate the weights of three objective optimization functions. Finally, the TOPSIS Algorithm is applied to obtain the optimal lane change trajectory. The simulations are conducted, and the results demonstrate that the proposed method can generate a satisfactory trajectory for automatic lane changing actions.
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Gao, Rui, Wei Zhang, Guofu Wang, and Xiaohuan Wang. "Experimental Research on Motion Analysis Model and Trajectory Planning of GLT Palletizing Robot." Buildings 13, no. 4 (2023): 966. http://dx.doi.org/10.3390/buildings13040966.
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To improve wood structure processing efficiency, a palletizing robot suitable for loading and unloading glued laminated timber (GLT) has been developed. The robot comprises a six-axis connecting rod mechanism and a sponge sucker as a grasping actuator, which can enable the intelligent automatic loading and unloading and palletizing operations for small-sized GLT. Matlab robotics was used to construct the kinematic model of the GLT loading and unloading robot. Based on Matlab and Monte Carlo methods, the robot workspace was simulated and analyzed to determine the scope of the robot workspace. Using the high-order quintic and sixtic polynomial curve interpolation method, the trajectory of wood structure parts in the process of loading and unloading operations was planned, respectively, under the two conditions of staying and not staying. Tests verified that the simulation results of the pose of the end-effector were consistent with the actual pose of the robot. The robot’s working range could be analyzed intuitively and effectively. The robot’s operation trajectory planning provides data support and a parameter basis for the automatic control and program design of a loading, unloading and palletizing robot.
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Wu, Chien-Sheng, Zih-Yun Chiu, and Jing-Sin Liu. "Time-Optimal Trajectory Planning along Parametric Polynomial Lane-Change Curves with Bounded Velocity and Acceleration: Simulations for a Unicycle Based on Numerical Integration." Modelling and Simulation in Engineering 2018 (November 19, 2018): 1–19. http://dx.doi.org/10.1155/2018/9348907.
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G2 lane-change path imposes symmetric conditions on the path geometric properties. This paper presents the comparative study of time-optimal velocities to minimize the time needed for traversal of three planar symmetric parametric polynomial lane-change paths followed by an autonomous vehicle, assuming that the neighboring lane is free. A simulated model based on unicycle that accounts for the acceleration and velocity bounds and is particularly simple for generating the time-optimal path parameterization of each lane-change path is adopted. We base the time-optimal trajectory simulations on numerical integration on a path basis under two different end conditions representing sufficient and restricted steering spaces with remarkable difference in allowable maximum curvature. The rest-to-rest lane-change maneuvering simulations highlight the effect of the most relevant path geometric properties on minimal travel time: a faster lane-change curve such as a quintic Bezier curve followed by a unicycle tends to be shorter in route length and lower in maximum curvature to have achievable highest speed at the maximum curvature points. The results have implications to path selection for parallel parking and allow the design of continuous acceleration profile via time scaling for smooth, faster motion along a given path. This could provide a reference for on-road lane-change trajectory planning along a given path other than parametric polynomials for significantly more complex, complete higher-dimensional highly nonlinear dynamic model of autonomous ground vehicle considering aerodynamic forces, tire and friction forces of tire-ground interaction, and terrain topology in real-world.
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Zhang, Lei, Guangyao Ouyang, and Zhaocai Du. "Kinematics decoupling analysis of a hyper-redundant manipulator driven by cables." Mechanical Sciences 12, no. 2 (2021): 1017–26. http://dx.doi.org/10.5194/ms-12-1017-2021.
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Abstract. The mapping relationship between the driving space and the workspace is essential for the precise control of a cable-driven hyper-redundant robot. For a hyper-redundant robot driven by cables, the relationships between the driving space and the joint space and between the joint space and the workspace were studied. A joint-decoupling kinematics analysis method was proposed and a kinematic analysis was presented. Based on the analysis of the coupling effect between the cable-driving space and the joint space, a decoupling analysis of the whole cable-driving space and joint space was conducted to eliminate the coupling effect between the joints, and the mapping relationship between the driving cables and the joint angles was obtained. Given the initial and target orientations of the hyper-redundant robot, the variation law for each joint angle was obtained using quintic polynomial trajectory planning and the pseudo-inverse Jacobian matrix, and then the driving cable variation law could be solved. Based on the results, the joint angle changes and the workspace trajectories were solved in turn. By comparing with the initial trajectory, the simulation results verified the appropriateness of the decoupling analysis.
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Zhang, Kaige, Yanjun Liu, Hua Jia, Feng Yan, and Gang Xue. "Research on a Three-Dimensional Fuzzy Active Disturbance Rejection Controller for the Mechanical Arm of an Iron Roughneck." Processes 11, no. 5 (2023): 1409. http://dx.doi.org/10.3390/pr11051409.
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In the position control of the mechanical arm of an iron roughneck (MAIR), a controller with high responsiveness, high accuracy, and high anti-interference capability is necessary. An MAIR consists of two proportional-valve-controlled single-extension (PVCSE) hydraulic cylinders, and a traditional proportional–integral–derivative (PID) controller cannot easily achieve the accuracy and robustness requirements of the hydraulic cylinders. In this paper, a three-dimensional fuzzy active disturbance rejection controller (TF-ADRC) is proposed for an MAIR, which adds a three-dimensional fuzzy module to a classical active disturbance rejection controller (ADRC) to adjust the controller output according to the tracking of differential deviation, deviation change rate, and deviation change acceleration rate. Firstly, the trajectory planning of the MAIR was carried out using the quintic polynomial interpolation method to improve the smoothness of the target trajectory. Then, the reliability of the established model was verified by experiments. Finally, the comprehensive performance of a PID controller, fuzzy PID controller, ADRC, and TF-ADRC were compared based on the AMESim-Simulink model. The system with the TF-ADRC exhibits higher position control accuracy and better anti-interference capability than the system with a PID or Fuzzy PID controller, and accuracy is higher compared with the common ADRC.
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Sadiq, Ahmed T., and Firas A. Raheem. "Robot Arm Path Planning Using Modified Particle Swarm Optimization based on D* algorithm." Al-Khwarizmi Engineering Journal 13, no. 3 (2017): 27–37. http://dx.doi.org/10.22153/kej.2017.02.001.
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Abstract
 Much attention has been paid for the use of robot arm in various applications. Therefore, the optimal path finding has a significant role to upgrade and guide the arm movement. The essential function of path planning is to create a path that satisfies the aims of motion including, averting obstacles collision, reducing time interval, decreasing the path traveling cost and satisfying the kinematics constraints. In this paper, the free Cartesian space map of 2-DOF arm is constructed to attain the joints variable at each point without collision. The D*algorithm and Euclidean distance are applied to obtain the exact and estimated distances to the goal respectively. The modified Particle Swarm Optimization algorithm is proposed to find an optimal path based on the local search, D* and Euclidean distances. The quintic polynomial equation is utilized to provide a smooth trajectory path. According to the observe results, the modified PSO algorithm is efficiently performs to find an optimal path even in difficult environments.
 
 Keywords: D*, Free Cartesian Space, Path Planning, Particle Swarm Optimization (PSO), Robot Arm.
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Wang, Tao, Dayi Qu, Hui Song, and Shouchen Dai. "A Hierarchical Framework of Decision Making and Trajectory Tracking Control for Autonomous Vehicles." Sustainability 15, no. 8 (2023): 6375. http://dx.doi.org/10.3390/su15086375.
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Most of the existing research in the field of autonomous vehicles (AVs) addresses decision making, planning and control as separate factors which may affect AV performance in complex driving environments. A hierarchical framework is proposed in this paper to address the problem mentioned above in environments with multiple lanes and surrounding vehicles. Firstly, high-level decision making is implemented by a finite-state machine (FSM), according to the relative relationship between the ego vehicle (EV) and the surrounding vehicles. After the decision is made, a cluster of quintic polynomial equations is established to generate the path connecting the initial position to the candidate target positions, according to the traffic states of the EV and the target vehicle. The optimal path is selected from the cluster, based on the quadratic programming (QP) framework. Then, the speed profile is generated, based on the longitudinal displacement–time graph (S–T graph), considering the vehicle motion state constraints and collision avoidance. The smoothed speed profile is created through another QP formulation, in the space created by the dynamic-programming (DP) method. Finally, the planned path and speed profile are combined and sent to the lower level control module, which consists of the linear quadratic regulator (LQR) for lateral trajectory tracking control, and a double PID controller for longitudinal control. The performance of the proposed framework was validated in a co-simulation environment using PreScan, MATLAB/Simulink and CarSim, and the results demonstrate that the proposed framework is capable of addressing most ordinary scenarios on a structured road, with reasonable decisions and controlling abilities.
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Yang, Guo, Shihuan Liu, Ming Ye, Chengcheng Tang, Yi Fan, and Yonggang Liu. "A Game Lane Changing Model Considering Driver’s Risk Level in Ramp Merging Scenario." World Electric Vehicle Journal 14, no. 7 (2023): 172. http://dx.doi.org/10.3390/wevj14070172.
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A ramp merging decision as an important part of the lane change model plays a crucial role in the efficiency and safety of the entire merging process. However, due to the inevitability of on-ramp merging, the limitations of the road environment, and the conflict between the merging vehicle and the following vehicle on the main road, it is difficult for human drivers to make optimal decisions in complex merging scenarios. First, based on the NGSIM dataset, a gain function is designed to represent the interaction between the ego vehicle (EV) and the surrounding vehicles, and the gain value is then used as one of the characteristic parameters. The K-means algorithm is employed to conduct a cluster analysis of the driving style under the condition of changing lanes. This paper models the interaction and conflict between the ego vehicle (vehicle merging) and the mainline lagging vehicle as a complete information non-cooperative game process. Further, various driving styles are coupled in the ramp decision model to mimic the different safety and travel efficiency preferences of human drivers. After EV decision-making, a quintic polynomial method with multi-constraints is proposed to implement merging trajectory planning. The proposed algorithm is tested and analyzed in an on-ramp scenario, and the results demonstrate that drivers with different driving styles can make correct decisions and complete the ramp merging. The changing trend of the speed and trajectory tests are also in line with the features of the driver’s driving style, offering a theoretical foundation for individualized on-ramp merging decisions.
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Han, Zexuan, Jiageng Ruan, Ying Li, He Wan, Zhenpeng Xue, and Jinming Zhang. "Active Collision-Avoidance Control Based on Emergency Decisions and Planning for Vehicle–Pedestrian Interaction Scenarios." Sustainability 17, no. 5 (2025): 2016. https://doi.org/10.3390/su17052016.
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Safe driving and effective collision avoidance are critical challenges in the development of autonomous driving technology. As the dynamic interactions between vehicles and pedestrians become increasingly complex, making rational decisions and accurately executing planning and control in emergency situations has become a core issue for sustainable development relating to traffic mobility and safety. This paper proposes an active collision-avoidance control strategy based on emergency decisions and planning in the context of vehicle–pedestrian interactions. A safety-distance model is developed with consideration given to the dynamic interactions between these two entities, and an emergency-decision mechanism is designed using the integration of priority rules. To generate smooth collision-avoidance trajectories, a quintic polynomial method is employed to construct trajectory clusters that meet the desired specifications. Moreover, a multi-objective optimization value function which considers multiple factors comprehensively is used to select the optimal path. To enhance collision-avoidance control accuracy, an RBF (radial basis function)–optimized SMC (sliding mode control) algorithm is introduced. Additionally, an FD-SF (force demand–based speed feedback) algorithm is designed to accurately track the longitudinal braking path. The results indicate that the proposed strategy can generate efficient, comfortable, and smooth optimal collision-avoidance paths, significantly improving vehicle response speed and control accuracy.
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G, Perumalsamy, Visweswaran P, Deepakkumar, Joseph Winston S, and Murugan S. "Selection of smooth motion profile for a tube locator module of an inspection device." IAES International Journal of Robotics and Automation (IJRA) 11, no. 3 (2022): 181–95. https://doi.org/10.11591/ijra.v11i3.pp181-195.
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The Prototype Fast Breeder Reactor steam generators inspection system has seven modules. In this, tube locator module is a planar serial two-link robotic arm, which is used to place the eddy current probe above the steam generators tube hole in the tube sheet region. The trajectory planning of the two-link robotic arm is one of the important tasks, so the peak velocity, peak acceleration, peak jerk of various motion profiles for a given distance has to be selected properly for smooth motion and to avoid actuator saturation. The fifth-order polynomial gives lower acceleration and velocity than the jerk-limited S-curve. In this paper, the comparison of peak values of kinematic variables (velocity, acceleration, and jerk) for different motion profiles has been presented.
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Cui, Yu Jie. "Research on the Trajectory Planning of the 4-DOF Manipulator." Advanced Materials Research 317-319 (August 2011): 734–37. http://dx.doi.org/10.4028/www.scientific.net/amr.317-319.734.
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Based on kinematics analysis, trajectory planning of a 4-DOF manipulator is researched on in this paper. Quintic polynomials is adopted to plan trajectory. The trajectory simulation of the manipulator is realized through using SimMechanics toolbox in MATLAB . The simulation experiments show the correctness and feasibility of the kinematics equations and algorithm of the manipulator trajectory planning.
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Hu, Lin, Jie Wang, Jing Huang, Pak Kin Wong, and Jing Zhao. "Lane Change Trajectory Planning for Intelligent Electric Vehicles in Dynamic Traffic Environments: Aiming at Optimal Energy Consumption." Sustainability 17, no. 9 (2025): 4235. https://doi.org/10.3390/su17094235.
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With the reduction in battery costs and the widespread application of artificial intelligence, the adoption of new-energy vehicles is accelerating. Integrating energy consumption optimization into the process of intelligent development is of great significance for sustainable development. This paper, considering the regenerative braking characteristics of electric vehicles and the time-varying nature of surrounding obstacle vehicles during lane changes, proposes a segmented real-time trajectory-planning method combining optimal control and quintic polynomials. At the beginning of the lane change, a safe intermediate position is calculated based on the speed and position information of the ego vehicle and the leading obstacle vehicle in the current lane. The trajectory optimization problem from the starting point to the intermediate position is formulated as an optimal control problem, resulting in the first segment of the trajectory. Upon reaching the intermediate position, the endpoint range is determined based on the speed and position information of the leading and trailing obstacle vehicles in the target lane. Multiple trajectories are then generated using quintic polynomials, and the optimal trajectory is selected as the second segment of the lane-changing trajectory. Experimental results from a driving simulator show that the proposed method can reduce energy consumption by approximately 40%.
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Jin, Ma, Mingcheng Qu, Qingyang Gao, Zhuo Huang, Tonghua Su, and Zhongchao Liang. "Advanced Trajectory Planning and Control for Autonomous Vehicles with Quintic Polynomials." Sensors 24, no. 24 (2024): 7928. https://doi.org/10.3390/s24247928.
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This paper focuses on the design of vehicle trajectories and their control systems. A method based on quintic polynomials is utilized to develop trajectories for intelligent vehicles, ensuring the smooth continuity of the trajectory and related state curves under varying conditions. The construction of lateral and longitudinal controllers is discussed, which includes a tracking error model derived from the two-degree-of-freedom dynamic model of a two-wheeled vehicle and the application of the Frenet coordinate system transformation. The vehicle tracking performance is regulated by these controllers. Experimental verification on a small intelligent vehicle platform operating on the Ackermann steering principle was conducted. The results confirm the tracking performance of the controllers under different conditions and validate the effectiveness and feasibility of the overall framework of the study.
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Chen, Mingfang, Kaixiang Zhang, Sen Wang, Fei Liu, Jinxin Liu, and Yongxia Zhang. "Analysis and Optimization of Interpolation Points for Quadruped Robots Joint Trajectory." Complexity 2020 (July 1, 2020): 1–17. http://dx.doi.org/10.1155/2020/3507679.
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Trajectory planning is the foundation of locomotion control for quadruped robots. This paper proposes a bionic foot-end trajectory which can adapt to many kinds of terrains and gaits based on the idea of trajectory planning combining Cartesian space with joint space. Trajectory points are picked for inverse kinematics solution, and then quintic polynomials are used to plan joint space trajectories. In order to ensure that the foot-end trajectory generated by the joint trajectory planning is closer to the original Cartesian trajectory, the distributions of the interpolation point are analyzed from the spatial domain to temporal domain. An evaluation function was established to assess the closeness degree between the actual trajectory and the original curve. Subsequently, the particle swarm optimization (PSO) algorithm and genetic algorithm (GA) for the points selection are used to obtain a more precise trajectory. Simulation and physical prototype experiments were included to support the correctness and effectiveness of the algorithms and the conclusions.
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Guo, Jin Chao, Zheng Liu, and Guang Zhao Cui. "A Mathematical Modeling and Optimization Approach for Trajectory Planning of Robot Manipulators." Applied Mechanics and Materials 157-158 (February 2012): 1388–92. http://dx.doi.org/10.4028/www.scientific.net/amm.157-158.1388.
Full textAbstract:
This paper presents a method for the problem of optimal trajectory planning of redundant robot manipulators in the presence of fixed obstacles. Quadrinomial and quintic polynomials are used to describe the segment of the trajectory. Cultural based PSO algorithm (CBPSO) is proposed to design a collision-free trajectory for planar redundant manipulators. CBPSO optimizes the trajectory and ensures that obstacle avoidance can be achieved. Simulations are carried out for different obstacles to prove the validity of the proposed algorithm. Different test data generated by GA, QPSO and CBPSO are provided with a tabular comparison. Simulation studies show CBPSO has potential online usage in engineering and distinct fast computation speed compared with the other two algorithms. Results demonstrate the effectiveness and capability of the proposed method in generating optimized collision-free trajectories.